$\dfrac{ r + 2s }{ -5 } = \dfrac{ -4r - t }{ -4 }$ Solve for $r$.
Solution: Multiply both sides by the left denominator. $\dfrac{ r + 2s }{ -{5} } = \dfrac{ -4r - t }{ -4 }$ $-{5} \cdot \dfrac{ r + 2s }{ -{5} } = -{5} \cdot \dfrac{ -4r - t }{ -4 }$ $r + 2s = -{5} \cdot \dfrac { -4r - t }{ -4 }$ Multiply both sides by the right denominator. $r + 2s = -5 \cdot \dfrac{ -4r - t }{ -{4} }$ $-{4} \cdot \left( r + 2s \right) = -{4} \cdot -5 \cdot \dfrac{ -4r - t }{ -{4} }$ $-{4} \cdot \left( r + 2s \right) = -5 \cdot \left( -4r - t \right)$ Distribute both sides $-{4} \cdot \left( r + 2s \right) = -{5} \cdot \left( -4r - t \right)$ $-{4}r - {8}s = {20}r + {5}t$ Combine $r$ terms on the left. $-{4r} - 8s = {20r} + 5t$ $-{24r} - 8s = 5t$ Move the $s$ term to the right. $-24r - {8s} = 5t$ $-24r = 5t + {8s}$ Isolate $r$ by dividing both sides by its coefficient. $-{24}r = 5t + 8s$ $r = \dfrac{ 5t + 8s }{ -{24} }$ Swap signs so the denominator isn't negative. $r = \dfrac{ -{5}t - {8}s }{ {24} }$